Question

which of these triangle pairs can be mapped to each other using a single translation?

Explanation:

Step1: Recall translation property

A translation is a rigid - motion that moves every point of a figure the same distance in the same direction. Corresponding sides and angles of the two triangles in a translation are congruent and have the same orientation.

Step2: Analyze triangle pairs

In a translation, the pre - image and the image have the same shape, size, and orientation. We need to look for two triangles where one can be slid to coincide with the other without rotation or reflection. If the triangles have the same orientation (i.e., the order of the vertices in a clock - wise or counter - clockwise direction is the same) and are congruent, they can be mapped by a translation.

However, since no other triangle pairs are shown in the provided image, we assume we are working with the two triangles $\triangle CPN$ and $\triangle CED$. We check for congruence and orientation. If the triangles are congruent (by SSS, SAS, ASA, AAS, or HL criteria) and have the same orientation, they can be mapped by a translation.

Let's assume we have determined that they are congruent and have the same orientation.

Answer:

The triangle pair that has the same orientation and is congruent can be mapped to each other using a single translation. Without seeing all the options, if $\triangle CPN$ and $\triangle CED$ are congruent and have the same orientation, they are the answer.